Friday, April 04, 2008

Ma vie en prose

Many, and over-ripe!

If this young man expresses himselfin terms too deep for me,Why, what a very singularly deep young manthis deep young man must be!

Life has been kind to faux mathematician David Berlinski. Reviewers praised the turgid but high-flown prose of A Tour of the Calculus to the skies, fooled by the author's ruffles and flourishes into thinking they were learning something about mathematics. I'm jealous, of course. Perhaps I should learn a lesson from him and tart up my writing.

But no. I have too much self-respect.

On the other hand, no one else seems to have as much respect for David Berlinski as David Berlinski himself. I inadvertently discovered more evidence of this while innocently browsing the offerings of a local bookstore. There on the table was a paperback edition of Infinite Ascent, Berlinski's venture into the world of math history. Struggling through Tour was all the exposure I felt I needed to his ham-handed treatment of mathematical topics, but I didn't resist the impulse to pick up the book and page through it. On page 106, I encountered a gemlike example of Berlinski's lapidary skill (note particularly the sentence which I render in bold):

Like a Parisian jeweler setting out the rarest of stones, he published only those of his papers that he believed had reached a state of formal perfection and lucidity.

It is a policy that I myself follow.

Berlinski is talking about Gauss (and himself!) here. Carl Friedrich Gauss is a towering figure in mathematics—the Prince of Mathematicians—who took seriously his motto of “Few, but ripe” in his approach to publishing his discoveries.

Berlinski fancies himself cut from the same cloth. He hasn't even the mild grace to say “It is a policy that I myself strive to follow.” Oh, no! Gauss's policy is his own. (Please to overlook the fact that he precedes this claim with a sentence that eloquently testifies to the contrary.)

I laughed aloud in the midst of the bookstore, fished a scrap of paper out of my pocket, and jotted down Berlinski's deadly example of deathless prose for the uncharitable purpose of making fun of it. And now I have done so.

But let us not stop there. Perhaps the passage in Infinite Descent is a fluke, an exception to the author's Gaussian standard. Let's peek into A Tour of the Calculus, shall we?

My copy has 314 pages. The random number generator on my HP calculator suggests I look at page 280. Can I find a silly sentence on this randomly selected page? How about this one?

This simple and dramatic appeal to the area underneath a curve succeeds not only in creating a new function—that was guaranteed by the very definition of the indefinite integral—but in creating a new function with precisely the properties required by the natural logarithm, so that the appeal to the function 1/t and the indefinite integral suggests more than anything else an actor slapping on grease paint in what seems a slap-dash way only to emerge moments later as precisely the character in a Shakespearean play whose vivid features figure in the program notes.

Bravo! Author! Author! Gauss has met his match! [Snicker]

I swear I am not cherry-picking. I really let my calculator select that page. Once more unto the breach, dear friends. My calculator chooses page 227. What ripeness do we find thereon? This ripeness:

“Antidifferentiation is an operation that involves a reversal of form,” I say, “and if a pictorial image is wanted it should be drawn from the world of fencing, as when the fencing master thrusts—differentiation—and with an enigmatic smile playing on his features after his opponent murmurs touché, backs up and retracts his elegant foil—antidifferentiation.”

That's quite a heaping helping of pellucid prose, ain't it? This is what prompted the San Francisco Chronicle to claim that Berlinski's “writing is so clean and powerful.” Touché! (Perhaps in la tête.)

Words fail me, although not in quite the way that they fail Berlinski. People fall all over themselves to declare him an expository genius. We can expect similar paroxysms of delight over his latest book, an attack on nonbelievers: The Devil's Delusion: Atheism and its Scientific Pretensions. I do not have this new volume (which carries the delightful publication date of April Fool's Day), but it's further evidence of Berlinski's utter inability to catch himself at self-parody. He has been most notable in recent years for his scientific pretensions as a senior fellow of the Discovery Institute's Center for Science and Culture. Despite being a self-professed agnostic, Berlinski specializes in giving aid and comfort to the Discovery Institute's theistic creationists, lending his supposed scientific credentials (degrees in math and philosophy) to their cause. Hence the new book. No doubt The Devil's Delusion is one of his greatest works.

5 comments:

I went to MathSciNet and checked out mathematical publications associated with this genius. Not much to look at.

Berlinski, David Newton's gift. How Sir Isaac Newton unlocked the system of the world. Free Press, New York, 2000. xviii+217 pp.

Part of the review: Though one does not have to use this book for scholarly work, it is disappointing to read inaccuracies such as the following: "By 1667, Newton had collected his thoughts on infinite series in a long manuscript--- On the analysis of infinite series" (p. 76). The title is wrongly translated: the analysis is by infinite series and not of them. Whiteside has tentatively suggested a dating not preceding the early summer of 1669 [see I. Newton, The mathematical papers of Isaac Newton. Vol. II, Cambridge Univ. Press, London, 1968; MR0228320 (37 \#3901) (p. 206, note)]. Without an explanation, Berlinksi proposes his dating.

Berlinski, David The advent of the algorithm. The idea that rules the world. Harcourt, Inc., New York, 2000. xxii+345 pp.

Part of the review: There are, however, too many things to be "endured" for the book to receive a full endorsement---from tedious discussions of logical calculi to incorrect formulations of the conversion rules for the lambda-calculus, from an unsatisfactory definition of primitive recursive functions to the claim that Gödel already in 1931 gave "for the first time" a precise mathematical description of the notion of an algorithm. These are just examples where important technical material is not properly "under control" and where significant historical matters are not accurately presented.

Berlinski, David Mathematical models of the world. Mathematical methods of the social sciences. Synthese 31 (1975), no. 2, 211--227.

Review: This paper is written like a literary paper with neither sections nor key words so that it is really difficult to grasp by a reader who is accustomed to present scientific journals. As far as the reviewer understands, this article is a critical survey of some models which are presently used for modelling practical dynamic systems or, as the author says, "models of the world". The concepts of "well posed problems", "structural stability" in Thom's sense, and "asymptotic stability" are analyzed in a synthetic overview, and some interesting questions are raised concerning the theoretical assumptions of some approaches. For instance, the assertion that only structurally stable models are of interest, may be questionable in some instances. The example of meteorology is expanded, qualitatively of course, to illustrate various questions such as the "problem of error", the "predictability limits", and the "average escape time". The paper ends with a summary of Zeeman's point of view on the necessity of using catastrophe theory in the study of social and political life.

From the viewpoint of the reviewer, attractive as it is, catastrophe theory is not fully fathomed, and its practical implications will not be clearly exhibited until its connection with partial differential equations is shown.

I shudder at the notion that some poor students might be required to learn calculus from the writings of this apparent afficianado (sp) of "It was a dark and stormy night..."

What baffles me about Berlinski and many others is, how do mathematicians and engineers, in particular, envision themselves as experts in evolutionary biology? Do they really believe that they somehow know more than the folks in the trenches?

I'm an engineer training to be a geologist, and I can't imagine some biologist saying, "no, you're all wrong about earthquake hazards, XYZ predicted earthquake isn't going to happen." So how can people like Berlinski sleep at night? Have they no humility whatsoever?????

Back in the days of Castles and Dragons when I was an undergrad, one of my calculus instructors remarked (in a private conversation) that the only people who believed in absolute truth were mathematicians and fundamentalist Christians. At the time, I didn't understand how right he was.

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I consistently come away in awe of how eloquently you write, and how you make choosing exactly the right word seem so effortless. You also seem to find subject matter in a wide variety of places, and you link contemporary and long-past events in unexpected ways.